Combined minimization of intersymbol interference (ISI) and adjacent channel interference (ACI)

ABSTRACT

Adaptive windowing of insufficient cyclic prefix (CP) for joint minimization of intersymbol interference (ISI) and adjacent channel interference (ACI) is provided. The proposed subcarrier specific windowing scheme improves the signal-to-interference ratio (SIR) even when the cyclic prefix (CP) is insufficient. Average optimal window lengths depend only on the power density profiles (PDPs), and although instantaneous optimal window lengths depend on users&#39; channel impulse responses (CIRs), fluctuation is little. Therefore, subcarrier specific windowing outperforms fixed windowing, even with outdated window lengths in the case of powerful interferers.

CROSS-REFERENCE TO RELATED APPLICATIONS

This nonprovisional application claims priority to U.S. ProvisionalPatent Application No. 62/569,220, entitled “Adaptive Utilization ofInsufficient Cyclic Prefix (CP) For Joint Minimization of IntersymbolInterference (ISI) And Adjacent Channel Interference (ACI)”, filed Oct.6, 2017 by the same inventors, the entirety of which is incorporatedherein by reference.

FEDERALLY SPONSORED RESEARCH OR DEVELOPMENT

This invention was made with government support 1609581 awarded by theNational Science Foundation. The Government has certain rights in theinvention.

BACKGROUND OF THE INVENTION

Conventional orthogonal frequency division multiplexing (OFDM) receiversare designed assuming the cyclic prefix (CP) is longer than the maximumexcess delay (MED) of the desired users channel, thereby reducingintersymbol interference (ISI). Users in adjacent bands are assumed tocause negligible adjacent channel interference (ACI). This is achievedby avoiding channels with maximum excess day longer than the cyclicprefix by elongating the cyclic prefix durations, such as theextended-CP option in Long Term Evolution (LTE). Possible adjacentchannel interference due to interferers in adjacent bands are eithermitigated using interference cancellation or avoided by increasing guardbandwidth until adjacent channel interference power becomes negligibleor suppressed.

There are numerous approaches known for suppressing ACI. The mostprominent approach is windowing, which is popular due to its lowcomputational complexity and efficacy. Windowing can be applied at thetransmitter to reduce out-of-band (OOB) emission and corresponding ACIbefore it eventuates, or alternatively, windowing can be used at thereceiver to reject present ACI. However, known windowing techniquesutilize the same window function for all subcarriers, while it is knownthat edge subcarriers are critical in out-of-band emissions and are moreprone to present ACI. Subcarrier specific windowing (SSW) techniques atboth the transmitter and receiver are known in the art. However, theknown SSW implementations assume that the cyclic prefix (CP) is longerthan the maximum excess delay (MED) of the channel, to accommodatewindowing and limit the window length to the guard interval that is notdisturbed by multipath reception. Implementations of subcarrier specificwindowing are also known to allocate additional samples for windowing,thereby reducing spectral efficiency, which is undesirable.

Cellular communication standards beyond 5G are envisioned tosimultaneously provide diverse services, with various requirements, to amyriad of devices. Increasing spectral efficiency is crucial toeffectively supporting the projected number of devices, particularly inlower carrier frequencies, thereby favoring reduced guards. Using cyclicprefix durations shorter than the users' maximum excess delay have beenproposed to satisfy the lower latency required by new services insystems beyond 5G, while also increasing spectral efficiency.

However, the conventional approaches do not address the requirements ofcommunication systems beyond 5G. Asynchronous, non-orthogonal waveformswith different parameterizations, referred to as numerologies, are alsoproposed to be used in adjacent bands to provide diverse services infuture standards. However, determining the adjacent channel interference(ACI) caused by such non-orthogonal numerologies has not been previouslyaddressed.

Accordingly, what is needed in the art is an improved system and methodthat addresses the additional requirements of communication systemsbeyond 5G, including increased spectral efficiency and adaptations fornon-orthogonal numerologies.

SUMMARY OF INVENTION

This invention addresses the interference resulting from resourceshortage in both the time domain and the frequency domain of a wirelesscommunication system, including insufficiency of guard time betweenconsecutive symbols of a user and insufficient guard band between userscommunicating in adjacent bands. Such resource shortage is expected tooccur in future cellular communication networks as studies have proposedshortening guard times to reduce latencies and reducing guard bands toincrease the number of users, as well addressing asynchronization.

In various embodiments, the present invention provides a method forwindowing of an Orthogonal Frequency Division Multiplexing (OFDM)-basedsignal, which includes, receiving, at a receiver, an OFDM-based signalcomprising a plurality of subcarriers, estimating an aggregate adjacentchannel interference (ACI) and intersymbol interference (ISI) at each ofthe plurality of subcarriers, estimating an optimal window duration foreach of the plurality of subcarriers, where in the optimal windowduration is the duration that minimizes the aggregate adjacent channelinterference (ACI) and intersymbol interference (ISI) at each of theplurality of subcarriers and performing, at the receiver, windowing ofeach of the plurality of subcarriers of the received OFDM-based signalby multiplying each of the plurality of subcarriers by the optimalwindow duration to generate a filtered OFDM-based signal.

In one embodiment, the optimal window duration for each of the pluralityof subcarriers is an instantaneous optimal window duration and theoptimal window duration is determined to be the duration that minimizesthe aggregate adjacent channel interference (ACI) and intersymbolinterference (ISI) at each of the plurality of subcarriers based uponthe power density profile (PDF) and the channel impulse (CIR) for eachof the plurality of subcarriers.

In another embodiment, the optimal window duration for each of theplurality of subcarriers is an instantaneous average window duration andthe optimal window duration is determined to be the duration thatminimizes the aggregate adjacent channel interference (ACI) andintersymbol interference (ISI) at each of the plurality of subcarriersbased upon the power density profile (PDF) for each of the plurality ofsubcarriers.

In an additional embodiment, the method of the present invention forwindowing of an Orthogonal Frequency Division Multiplexing (OFDM)-basedsignal may be performed at a transmitter prior to transmitting theOFDM-based signal over the communication channel.

The invention further includes, a receiver for windowing of anOrthogonal Frequency Division Multiplexing (OFDM)-based signal. In aparticular embodiment, the receiver includes, an analog to digitalmodule configured for receiving an OFDM-based signal comprising aplurality of subcarriers. The receiver further includes a receiverfilter coupled to the analog to digital module, the receiver filterconfigured for estimating an aggregate adjacent channel interference(ACI) and intersymbol interference (ISI) at each of the plurality ofsubcarriers, for estimating an optimal window duration for each of theplurality of subcarriers, where in the optimal window duration is theduration that minimizes the aggregate adjacent channel interference(ACI) and intersymbol interference (ISI) at each of the plurality ofsubcarriers and for performing windowing of each of the plurality ofsubcarriers of the received OFDM-based signal by multiplying each of theplurality of subcarriers by the optimal window duration to generate afiltered OFDM-based signal. The receiver additionally includes, ademodulation module coupled to the receiver filter, the demodulationmodule configured for receiving the filtered OFDM-based signal and fordemodulating each of the plurality of subcarriers of the OFDM-basedsignal.

The invention may additionally includes, a transmitter for windowing ofan Orthogonal Frequency Division Multiplexing (OFDM)-based signal. Thetransmitter may include, a modulation module configured to receive adigital signal to be transmitted, the modulation module configured tomodulate the digital signal to generate an OFDM-based signal comprisinga plurality of subcarriers. The transmitter may further include, atransmitter filter coupled to the modulation module, the transmitterfilter configured for estimating an aggregate adjacent channelinterference (ACI) and intersymbol interference (ISI) at each of theplurality of subcarriers, for estimating an optimal window duration foreach of the plurality of subcarriers, where in the optimal windowduration is the duration that minimizes the aggregate adjacent channelinterference (ACI) and intersymbol interference (ISI) at each of theplurality of subcarriers and for performing windowing of each of theplurality of subcarriers of the received OFDM-based signal bymultiplying each of the plurality of subcarriers by the optimal windowduration to generate a filtered OFDM-based signal. The transmitter mayadditionally include, a digital to analog module coupled to thetransmitter filter, the digital to analog module configured fortransmitting the filtered OFDM-based signal.

In this present invention, insufficient cyclic prefix is optimallyutilized to jointly minimize ISI and ACI, thereby adaptively addressingspectral efficiency requirements of systems beyond 5G and thecorresponding real-time conditions. In various embodiments, incident ISIcaused by insufficient CP is first determined, and ACI caused bydifferent numerologies in adjacent bands is then determined. Thecombined interference power for each subcarrier is then minimized tooptimize the solution.

BRIEF DESCRIPTION OF THE DRAWINGS

For a fuller understanding of the invention, reference should be made tothe following detailed description, taken in connection with theaccompanying drawings, in which:

FIG. 1 is a graphical illustration of the post-equalization

_(s){P_(n,d,0) ^(int)} and P_(n,d,0) ^(int)(s) for a realization, forL_(n,d,0) ^(W)=0∀n.

FIG. 2A is a graphical illustration of pre-window interference indesired user's signal for one realization.

FIG. 2B is a graphical illustration of pre-window interference indesired user's signal for mean of many realizations.

FIG. 3A is graphical illustration of a one realization for

/K and

_(s){P_(n,d,0) ^(int)} for L_(n:d,0) ^(W)={0,L_(d)^({circumflex over (f)}ix),

}.

FIG. 3B is a graphical illustration of a mean of many realizations for

/K and

_(j){

_(s){P_(n,i,0)}}for L_(n,j,0) ^(W)={0,L_(j) ^({circumflex over (f)}ix),

}.

FIG. 4 is a graphical illustration of SIR gain of receivers withL_(n,i,u) ^(W)={L_(i−1,u) ^({circumflex over (f)}ix),L_(u)^(âvf),L_(i,u) ^({circumflex over (f)}ix),

, L_(n,u) ^(âvs),

} over no windowing for different interferer power offsets.

FIG. 5 is an illustration of an OFDM-based system for implementing thevarious methods of the present invention.

DETAILED DESCRIPTION OF THE INVENTION

In various embodiments, the method of the present invention proposeswindowing the cyclic prefix (CP) at the receiver utilizing subcarrierspecific windowing. The specific duration of the window for eachsubcarrier is the duration that minimizes the aggregate interferencecaused by the insufficiency of the cyclic prefix, with respect to theeffective channel length, and the interference caused by asynchronouscommunication in adjacent bands.

In a practical scenario, multiple users are simultaneously transmittingdata to a base station of a communication network using finite durationelectromagnetic pulses. The electromagnetic pulses are modulated toadjacent frequency bands, utilizing a protocol commonly referred to asFrequency-Division Multiple Access (FDMA). FDMA assigns users anindividual allocation of one or several frequency bands, or channels.The data of each user that is transmitted on the channel(s) must bereceived separately at the receiver, because they use differentmulticarrier pulse shapes.

Due to the electromagnetic waves being reflected, scattered or sloweddown by physical objects, in addition to the variation in distancesbetween the user and the base station, multiple copies of the signalarrive at the receiver of the base station at various times havingdifferent complex gains, which is commonly referred to as multi-pathfading. In multi-path fading, if one symbol of the modulated signalinterferes with the reception pulse of the next symbol, intersymbolinterference (ISI) occurs.

Additionally, because the transmitted electromagnetic pulses used tocommunicate on the channel do not have infinite duration, they havenon-zero power beyond their allocated band. This non-zero power outsideof the assigned band of the user results in interference to the userscommunicating in these bands, which is commonly referred to as adjacentchannel interference (ACI).

The electromagnetic pulses transmitted on the channel are a function ofthe information (data) transmitted to the users. As such, theintersymbol interference (ISI) and the adjacent channel interference(ACI) are also dependent upon the information transmitted by both theuser of interest and the users operating in the adjacent bands.Additionally, time dispersion, or echoes, caused by multi-pathpropagation delays changes the received aggregate signal, which effectsthe reception of both the signal of interest and the reception of thesignals in the bands adjacent to the bands used by the signal ofinterest.

The inventive method formulates the calculation of expected interferencedue to any OFDM signal in the Gabor lattice and encloses the originalidea of windowing each subcarrier differently at the receiver, even inthe absence of undistorted cyclic prefix, to maximize signal tointerference ratio (SIR).

In a particular embodiment, a 1-indexed algebra is used where I_(N), isthe N×N identity matrix, 0_(N×M) is the N×M zero and 1_(N×M) is the N×Mones matrix. Conjugate, transpose and Hermitian operations are denotedby (⋅)*, (⋅)^(T) and (⋅)^(H), respectively. A⊙B is the Hadamard productof matrices A and B and A

B denotes the Hadamard division of A to B. X^(⊙) ² is the Hadamardproduct of matrix X with itself.

_(a){⋅} is the expectation operator over variable a. diag (c1, c2, . . ., cN) represents the N×N diagonal matrix with diagonal elements c1, c2,. . . , c_(N), toep ({right arrow over (A)}, {right arrow over (B)})denotes the Toeplitz matrix of which first column is {right arrow over(A)} and first row is {right arrow over (B)}, δ(⋅) is the Dirac deltafunction, N (μ;σ²) is the normal distribution with mean μ and varianceσ², and fliplr (⋅) is the function that flips a matrix from left toright, i.e., X_(M,n)=fliplr (X_(M,N−n+1)). All properties existing withsubscripts ⋅_(u) denote that the given matrix or vector is associatedwith the uth user.

Let s_(u)∈

^(Mu×Iu) denote the modulated data symbols, where M_(u) is number of uthuser's data subcarriers and I_(u) is the number of uth user's OFDMsymbols in a frame. Q_(u)∈

^(Nu×Mu) is uth user's subcarrier mapping matrix. A_(u)∈

^(Nu+Ku×Nu) is uth user's CP insertion matrix, consisting of:

$\begin{matrix}{A_{u} = \begin{bmatrix}\begin{matrix}0_{K_{u} \times {({N_{u} - K_{u}})}} & I_{K_{u}}\end{matrix} \\I_{N_{u}}\end{bmatrix}} & (1)\end{matrix}$in the case of no transmitter windowing, where K_(u) is the number of CPsamples. The CP removal and windowing matrix B_(L) _(n,i,u) _(W) ∈

^(N) ^(u) ^(×N) ^(u) ^(+K) ^(u) is shown in equation (2), whereL_(n,i,u) ^(W) ∈{0, 1, . . . , K_(u)} is the taper length of either sideof the window, in number of samples, used for the reception of the nthsubcarrier of ith OFDM symbol of uth user andW_({right arrow over (n)},i,u)∈

^(1×L) ^(n,i,u) ^(W) the receiver window coefficients, are calculatedusing W

${\left( {k;L_{n,i,u}^{W}} \right) = \left( {1 + {\cos\left( \frac{\pi\; k}{L_{n,i,u}^{W} + 1} \right)}} \right)},{k = 1},2,\ldots\mspace{14mu},L_{n,i,u}^{W},$which generates raised cosine window coefficients using taper lengthinstead of roll-off. Note that when L_(n,i,u) ^(W)=0, equation (2)simplifies to B₀=[0_(N) _(u) _(×K) _(u) I_(N) _(u) ], which is the CPremoval matrix without windowing.

$\begin{matrix}{B_{L_{n,i,u}^{W}} = \left\lbrack \begin{matrix}0_{N_{u} - {L_{n,i,u}^{W} \times K_{u}} - L_{n,i,u}^{W}} & 0_{N_{u} - {L_{n,i,u}^{W} \times L_{n,i,u}^{W}}} & I_{N_{u} - L_{n,i,u}^{W}} & 0_{N_{u} - {L_{n,i,u}^{W} \times L_{n,i,u}^{W}}} \\0_{{L_{n,i,u}^{W} \times K_{u}} - L_{n,i,u}^{W}} & {{diag}\left( {{fliplr}\left( W_{n,i,u} \right)} \right)} & 0_{{L_{n,i,u}^{W} \times N_{u}} - L_{n,i,u}^{W}} & {{diag}\left( W_{n,i,u} \right)}\end{matrix} \right\rbrack} & (2)\end{matrix}$h_({right arrow over (i)},u)∈

^(1×L) ^(u) denotes the CIR invariant during reception of thecorresponding OFDM symbol where L_(u) is the MED uth user experiences innumber of samples, which is obtained by

${h_{\overset{\rightarrow}{\iota},u}(k)} = {\sqrt{P_{u}\frac{1 - \alpha_{u}}{1 - \alpha_{u}^{L_{u}}}}\alpha_{u}^{k}{\overset{\rightarrow}{v}(k)}}$where P_(u) is the received power of uth user's signal α_(u) is theexponential decay rate of uth user's channel {right arrow over (v)}(k)∈

^(1×L) ^(u) ˜CN(0,1)∀k∈{0, 1, . . . , L_(u)−1} [10]. Then, h_(i,u)^(conv)∈

^(N) ^(u) ^(+K) ^(u) ^(×N) ^(u) ^(+K) ^(u) is the linear channelconvolution matrix bounded to one symbol duration,

$h_{i,u}^{conv} = {{{toep}\left( {\left\lbrack {h_{\overset{\rightarrow}{i},u}\mspace{14mu} 0_{{1 \times N_{u}}\overset{\rightarrow}{+}K_{u} - L_{u}}} \right\rbrack^{T},\left\lbrack {{h_{\overset{\rightarrow}{i},u}(0)}\mspace{14mu} 0_{{1 \times N_{u}}\overset{\rightarrow}{+}K_{u} - 1}} \right\rbrack} \right)}.}$h_({right arrow over (i)},u)∈

^(N) ^(u×1) is the channel frequency response (CFR) of uth user's ithOFDM symbol, which can be calculated as

$H_{\overset{\rightarrow}{i},u} = {\sqrt{N_{u}}{{F_{u}\left\lbrack {h_{\overset{\rightarrow}{i},u}\mspace{14mu} 0_{{1 \times N_{u}} - L_{u}}} \right\rbrack}^{T}.}}$Defining the ISI free condition as:K _(u) −L _(n,i,u) ^(W) ≥L _(u) ,∀n∈{1,2, . . . ,N _(u)}  (3)

Assume desired OFDM symbol is the dth OFDM symbol of 0th user. Let usfirst assume the absence of the interfering users, and equation (3) issatisfied. In this case the product B_(L) _(:d,O) _(W) h_(d,0) ^(conv)A₀results in the perfect circular channel convolution matrix h_(d,0)^(circ)∈

^(N) ⁰ ^(×N) ⁰ shown in equation (4).

$\begin{matrix}{h_{i,u}^{circ} = {{toep}\left( {\left\lbrack {h_{\overset{\rightarrow}{i},u}\mspace{14mu} 0_{{1 \times {\overset{\rightarrow}{N}}_{u}} - L_{u}}} \right\rbrack^{T},\left\lbrack {{h_{\overset{\rightarrow}{i},u}(0)}\mspace{14mu}{{fliplr}\left( \left\lbrack {{h_{\overset{\rightarrow}{i},u}\left( {{1\text{:}\mspace{14mu} L_{u}} - 1} \right)}\mspace{14mu} 0_{{1 \times {\overset{\rightarrow}{N}}_{u}} - L_{u}}} \right\rbrack \right)}} \right\rbrack} \right)}} & (4)\end{matrix}$

Furthermore, F₀B_(L) _(:d,O) ^(W)h_(d,0) ^(conv)A₀F₀ ^(H) results indiag ({right arrow over (H)}_(d,0)), where F_(u)∈

^(N×N) denotes the normalized fast Fourier transformation (FFT) matrixuth user uses in the generation and reception of OFDM symbols. Hence,ignoring the noise, the received symbols

$y_{:{,\overset{\rightarrow}{d},0}} = {{F_{0}B_{L_{:{,d,O}}^{W}}h_{d,0}^{conv}A_{0}F_{0}^{H}Q_{u}s_{:{,\overset{\rightarrow}{d},0}}} = {{{{diag}\left( {\overset{\rightarrow}{H}}_{d,0} \right)}s_{:{,\overset{\rightarrow}{d},0}}} = {{{\overset{\rightarrow}{H}}_{d,0} \odot s_{:{,\overset{\rightarrow}{d},0}}} \cdot y_{:{,\overset{\rightarrow}{d},0}}}}}$is equalized using zero forcing (ZF) equalization via a similar Hadamarddivision by CFR to obtain the symbol estimates ŝ_(:,d,0)∈

^(N) ⁰ ^(×1).

$\begin{matrix}{{\hat{s}}_{:{,d,0}} = {Q_{u}^{H}\left( {y_{:{,\overset{\rightarrow}{d},0}}{\hat{H}}_{d{.0}}} \right)}} & (5)\end{matrix}$where, Ĥ_(d.0) is the desired OFDM symbol's channel frequency response(CFR) that is estimated at the receiver.

In this present invention, although there would be residual ISI, asequation (3) is invalid, equalization will still be performed as inequation (5) and no interference cancellation technique, other thanreceiver windowing, is applied to reduce the ACI and residual ISI. Inthe scenario of interest, the received signal consists of the distorteddesired signal and interference from other signals, including ISI fromthe previous symbol, and ACI from signals in adjacent bands. One of thegoals of the present invention is to minimize the aggregation of thedistortion of the desired signal and the interference.

The distortion of the desired signal can be determined by calculatingthe difference between the signal that would have been received ifequation (3) was satisfied, and the actual received signal. If equation(3) was satisfied, the channel convolution matrix would have beenperfectly circular, and the received signal would bey_(:,{right arrow over (d)},0)=F₀h_(d,0) ^(circ)F₀^(H)Q_(u)s_(:,{right arrow over (d)},0). Then, the difference betweenthe perfect and effective circular channel convolution matrices when CPis added using equation (1) and removed using equation (2), forms thedistortion matrix h_(d,0) ^(dist)∈

^(N) ^(u) ^(×N) ^(u) , which is h_(d,0) ^(dist)=B_(L) _(n:i) _(w)h^(conv)A−h^(circ). Hence, the distortion in the nth subcarrier of thedesired OFDM symbol is found as y_(n,d,0)^({right arrow over (dist)})=F₀h_(d,0) ^(dist)F₀^(H)Q_(u)s_(:,{right arrow over (d)},0).

The ISI and ACI from all other signals are calculated by projectingsamples of each received OFDM symbol to the corresponding samples of thedesired OFDM symbol in this asynchronous scenario. Each received OFDMsymbol affects a total of

$\frac{\Delta\; f_{0}}{\Delta\; f_{u}}\left( {N_{u} + {K_{u}\left( {L_{u} - 1} \right)}} \right)$time samples. The channel output, including the CIR filter tail, iscalculated by left multiplying the transmit samples with

h i , u full ∈ Δ ⁢ ⁢ f 0 Δ ⁢ ⁢ f u ⁢ ( N u + K u ⁡ ( L u - 1 ) ) × N u + K u ,where

${h_{i,u}^{full} = {{{toep}\left( {\left\lbrack {h_{\overset{\rightarrow}{i},u}\mspace{14mu} 0_{{1 \times N_{u}}\overset{\rightarrow}{+}K_{u} - 1}} \right\rbrack^{T},\left\lbrack {{h_{\overset{\rightarrow}{i},u}(0)}\mspace{14mu} 0_{{1 \times N_{u}}\overset{\rightarrow}{+}K_{u} - 1}} \right\rbrack} \right)}R}},$where

R ∈ Δ ⁢ ⁢ f 0 Δ ⁢ ⁢ f u ⁢ ( N u + K u ⁡ ( L u - 1 ) ) × 1is any resampling transform. Let

t i → , u ∈ Δ ⁢ ⁢ f 0 Δ ⁢ ⁢ f u ⁢ ( N u + K u ⁡ ( L u - 1 ) ) × 1denote the time indices of the received samples that contains energyfrom the samples of the ith OFDM symbol of uth user. Then, a projectionmatrix

∏ i , u : d , 0 ⁢ ∈ N 0 + K 0 × Δ ⁢ ⁢ f 0 Δ ⁢ ⁢ f u ⁢ ( N u + K u ⁡ ( L u - 1 ))formed such that the misaligned, asynchronous samples are projected ontothe received symbol:

$\begin{matrix}{{\prod\limits_{i,{u:d},0}\left( {g,j} \right)} = \left\{ \begin{matrix}{1,} & {{t_{\overset{\rightarrow}{d},0}(g)} = {t_{\overset{\rightarrow}{i},u}(j)}} \\{0,} & {o.w.}\end{matrix} \right.} & (6)\end{matrix}$

Thus, the aggregate interference on the nth subcarrier of the desiredsymbol is found as:

$\begin{matrix}{y_{n,d,0}^{\overset{\rightarrow}{int}} = {y_{n,d,0}^{\overset{\rightarrow}{dist}} + {\underset{\underset{{\{{i,u}\}} \neq {\{{d,0}\}}}{u,i}}{\sum\sum}F_{0}B_{L_{n,d,O}^{W}}{\prod\limits_{i,{u:d},0}{h_{i,u}^{full}A_{u}F_{u}^{H}Q_{u}s_{:{,\overset{\rightarrow}{i},0}}}}}}} & (7)\end{matrix}$

Using this formulation, the instantaneous interference power is easilycalculated if all parameters are known. Note that in the numericalverification of this work, sampling rates are matched using Fourierinterpolation, implying a Dirichlet kernel.

However, practically, information symbols of all users are unknown atthe time of reception and, as such, an estimate of the expectedinterference power is needed. To calculate this value, the followingstatistical conjecture is used:

Conjecture 1. The symbols transmitted using any subcarrier of any OFDMsymbol of any user are independent from each other and the usedmodulation is unit average power, i.e.,

{s_(n,i,u)s*_(n′,i′, u′)}=δ(n−n′)δ(i−i′)δ(u−u′)∀n, n′, i, i′, u, u′.

Conjecture 1 implies that, for a practical number of subcarriers, thevariance of their sum is the sum of their variances by the law of largenumbers. Each column of F^(H) contains the phase rotation of a normalrandom variable and the sum of variances of all columns yields the totalinterference power contributed to the symbol. Thus, the expectedaggregate interference to the nth received subcarrier of the desireduser is given in the nth column of

$\begin{matrix}\begin{matrix}{u,i} \\{\left\{ {i,u} \right\} \neq \left\{ {d,0} \right\}}\end{matrix} & (8) \\{{{\mathbb{E}}_{s}\left\{ P_{:{,d,0}}^{int} \right\}} = {{1_{\overset{\rightarrow}{1 \times}N}\left( {{F_{0}h_{d,0}^{dist}F_{0}^{H}Q_{u}s_{:{,\overset{\rightarrow}{d},0}}}}^{\odot 2} \right)^{T}} + {\sum{\sum{1_{\overset{\rightarrow}{1 \times}N}\left( {{F_{0}B_{L_{n,d,O}^{W}}{\prod\limits_{i,{u:d},0}{h_{i,u}^{full}A_{u}Q_{u}F_{u}^{H}}}}}^{\odot 2} \right)^{T}}}}}} & \;\end{matrix}$where the nth column of 1_({right arrow over (1×)}N)X^(T) contains thesum of all elements in the nth row of X.

In the proposed method of the present invention, the receiver is tosolve either of:

$\begin{matrix}\begin{matrix}{L_{n,i,u}^{\hat{SS}W} = {\arg_{L_{n,d,u}^{W}}\min}} & {{\mathbb{E}}_{s}\left\{ P_{n,d,u}^{int} \right\}}\end{matrix} & (9) \\\begin{matrix}{L_{n,u}^{\hat{av}s} = {\arg_{L_{n,i,u}^{W}}\min}} & {{\mathbb{E}}_{i}\left\{ {{\mathbb{E}}_{s}\left\{ P_{n,i,u}^{int} \right\}} \right\}}\end{matrix} & (10) \\\begin{matrix}{L_{d,u}^{\hat{{fi}\; x}} = {\arg_{L_{n,u,u}^{W}}\min}} & {{\mathbb{E}}_{n}\left\{ {{\mathbb{E}}_{s}\left\{ P_{n,d,u}^{int} \right\}} \right\}}\end{matrix} & (11) \\\begin{matrix}{L_{u}^{\hat{av}f} = {\arg_{L_{n,i,u}^{W}}\min}} & {{\mathbb{E}}_{i}\left\{ {{\mathbb{E}}_{n}\left\{ {{\mathbb{E}}_{s}\left\{ P_{n,i,u}^{int} \right\}} \right\}} \right\}}\end{matrix} & (12)\end{matrix}$subject to L _(n,i,u) ^(W)∈{0,1. . . ,K _(u)}  (13)

to find:

1) optimal subcarrier specific windows (SSWs) lengths for known channelimpulse responses (CIRs) from equation (9)

2) average subcarrier specific windows SSW lengths depending on users'power delay profiles (PDPs) from equation (10)

3) optimal window length for conventional “fixed” receiver windowingusing the same window lengths for all subcarriers for known channelimpulse responses (CIRs) from equation (11)

4) average fixed length depending on users' power delay profiles (PDPs)from equation (12).

The required computational complexity of the options decreases, alongwith the resulting performance, from option 1) down to option 4).

In the present invention, the instantaneous optimal window lengthsdepend upon the channel impulse responses (CIRs), however, the averageoptimal window lengths are obtained only for the power delay profiles(PDPs), wherein the PDPs are the mean of the magnitude of the CIRs overa plurality of OFDM symbols.

In most practical cases, the PDPs are simpler to obtain, as compared tothe full channel information. Accordingly, in the present invention, themagnitude alone can be used without the instantaneous phase of thechannel being know to determine the average optimal window lengths,wherein the magnitude is not instantaneous, but is instead the averagechannel magnitude over a number of symbols.

There are various means known in the art for obtaining the PDP of thesymbols, including but not limited to, equiweight averaging andexponential weighted averaging. In exponential weighted averaging, moreweight is placed on more recent symbols and weights are determined fromthe exponential function and interpolation between symbols, after aweighting period.

In the following analysis, the solutions to window length calculationsare not provided but performance gain is illustrated.

Provided the solutions are known, the subcarrier specific windowrequires additional

$\sum\limits_{L^{W} \in \; L^{S\hat{S}{W\backslash L_{i}^{\hat{f}{ix}}}}}\left( {{4L^{W}} + {\frac{N}{2}\log_{2}N}} \right)$multiplications and

$\sum\limits_{L^{W} \in \; L^{S\hat{S}{W\backslash L_{i}^{\hat{f}{ix}}}}}\left( {{2L^{W}} + {N\;\log_{2}N}} \right)$additions on top of fixed windowing, due to additional overlapping(first terms) and FFT operations (second terms).

An exemplary embodiment, with the following parameters, was simulated todemonstrate the gains of the proposed method of the present invention.In the exemplary embodiment, α_(u), CIRs and time offset between usersare randomized at each run. Ĥ_(i,u)=H_(i,u)∀i, u and

_(i){h_(i,u)h*_(i−Δi,u)}=P_(u)δ(Δi). P⁻¹=P₁ always, and are equal to 2P₀in the remaining figures, with the exception of FIG. 4. In the exemplaryembodiment, there is no guard band between any user, the firstsubcarrier of the user with a narrower bandwidth is located at the firstnull of the adjacent user's edge-most subcarrier. Additionally, in theexemplary embodiment, 2Δf⁻¹=Δf₀=Δf₁/2, where user indices distinguishtheir order in the spectrum. The rest of the variables are given in thesampling rate of user 0. N_({−1,0,1})={512, 256, 128},M_({−1,0,1})={123, 127, 31}, and K_({−1,0,1})={36, 18, 9} whereasL_({−1,0,1})={64, 32, 16}.

FIG. 1 illustrates the post-equalization expected aggregate interferencefor unknown signals 100 and the actual interference for known signals105, for a single realization of the aforementioned exemplaryembodiment. As shown, the expected interference calculations areaccurate in determining the actual interference, but a slight mismatchoccurs due to the dependence of the signal of interest on the multi-pathfading of the signal transmitted in the adjacent channel and theresulting adjacent channel interference (ACI) on the interfering users'signals.

The ISI power 110, consisting of both the distortion of the symbol ofinterest and the leakage from the preceding symbol of desired symbol,the ACI power 120 and the combined interference power of the ISI powerand the ACI power 115 at the subcarriers of the signal of interest areshown in FIG. 2A and FIG. 2B. In case of a single realization shown inFIG. 2A, the dependency of the users' signals on the instantaneouschannels of interfering users can be observed by the power offset at theedge subcarriers, although both interferers have the same transmitpowers. As the results are averaged over many realizations, as shown inFIG. 2B, the ISI power 125 becomes uniform throughout the subcarriersand the ACI power 135 becomes stronger at edges and weaker in innersubcarriers, resulting in the combined interference power of the ISIpower and the ACI power 130 over many realizations.

FIG. 1 illustrates the effect that echoes, or time dispersion, has onthe power of the received signal 105, caused by the multi-pathpropagation delay of the signals transmitted in the adjacent channels.Without multi-path fading, the power profile of the signal of interest115 would be as shown in FIG. 2A. Therefore, the state of the multi-pathfading caused by the echoes is critical to the determination of theamount of interference present on a received pulse of interest.

While it is known in the art to use optimal pulse shaping functions forindividual subcarriers to minimize ISI, the durations of the pulsesremained the same for all the subcarriers. As such, the dependence ofthe signal of interest on the information contained in the symbols andthe characteristics of the channel have not been considered in theprevious works.

The present invention addresses the echoes in the received pulse, whichresult from multi-path fading, in addition to the effect of themulti-path fading in the frequency domain, due to the channel. Invarious embodiments, the amount of adjacent channel interference (ACI)and intersymbol interference (ISI) that would be introduced into areceived pulse of interest can be found from equation (8). As such, theexpected aggregate interference (ACI+ISI) to the nth received subcarrierof the desired user resulting from the information of all the users ofthe channel and the channel response can be determined.

Assuming the information transmitted by the users may or may not beknown and the channel response may or may not be known, maximumlikelihood approximations can be used to determine the resultinginterference if:

1) The information is not known, but the channel is response is known.

2) The information and the channel response are known, but the powerdelay profile (PDF) of the channels are known.

3) Only the mean received power of each signal is known.

In order to identify an optimum window duration for each subcarrier thatminimizes the sum of the ACI and ISI at that subcarrier, it is necessaryto calculate the interference as a function of the information containedwithin the signal and the channel response.

In a particular embodiment, an iterative optimization method may beimplemented to determine the optimum window duration for each of thesubcarriers. In this embodiment, a memory of the receiver may store allthe corresponding pulse shapes for each of the subcarriers and theassociated window durations. A processor of the receiver may then beused to find the optimum window duration of the center subcarrier bystarting from no windowing and increasing the window length at eachiteration. The processor then solves for the expected aggregateinterference (equation (8)) using each saved pulse shape (variable B inequation (8)). The expected aggregate interference is determined basedupon what is known about the signal, such as the information containedin the signal and the channel impulse response (CIR). The operationcontinues by increasing the window length at each iteration, until thecalculation results in an increase in the expected aggregateinterference. It is then determined that the optimum duration of thewindow for the center subcarrier is the length prior to the lengthhaving an increased expected aggregate interference.

After determining the optimum duration of the window for the centersubcarrier of the user of interest, the method continues by solving forthe subcarriers adjacent to the center subcarrier. In solving for theoptimum duration window of adjacent subcarriers, the iterative processbegins by setting the duration of the adjacent subcarrier(s) to be equalto the optimum duration window of the center subcarrier, since theresult for the adjacent subcarrier(s) is not expected to change rapidlyfor adjacent subcarriers. Since the overall system is convex, the localminimum is equivalent to the global minimum. As such, progressing towardthe minimum value for each individual subcarrier approaches a globalsolution for all the subcarriers. Using the length of the centersubcarrier optimum duration window as a starting point for thedetermination of the optimum duration window for each adjacentsubcarrier insures an efficient computation of the global solution. Inthis iterative method, calculations for both shorter and longer windowdurations are made until the window duration that minimizes theestimated aggregate interference is determined for each subcarrieradjacent to the center subcarrier of the user's signal of interest. Themethod continues by finding the optimum window duration of eachsubcarrier of the user of interest, using the optimum window duration ofan adjacent subcarrier as the initial starting point for the iteration.

The results of the grid search for optimal subcarrier specific window(SSW) length for known channel impulse responses (CIRs), therebysatisfying equation (9), are shown in FIG. 3A and FIG. 3B, for the samerealization depicted in FIG. 2B. FIG. 3A illustrates the optimum windowduration 155 for one realization and the estimated aggregateinterferences 140, 145, 150 for various known parameters. FIG. 3Billustrates a mean of many realizations for the average optimum windowduration 175 and the mean estimated aggregate interferences 160, 165,170 for various known parameters. As shown, the results agree with thechannel dependency of optimal SSW lengths. As shown in FIG. 3B, longerwindow durations are required at the edge subcarriers.

The signal to interference ratio (SIR) gains of seven differentreceivers, over many power offsets, were calculated and the gain vs. a“no-windowing scenario” is presented in FIG. 4. As shown, implementingSSW guarantees higher gain than fixed windowing, with current andaverage optimal length and outdated lengths become robust as interferersbecome more powerful. Since the channel impulse response (CIR) isestimated at the receiver and then fed back to the transmitter, however,the estimated CIR cannot be used directly to select the parameters forthe adaptive transmission because is quickly becomes outdated due to therapid channel variation caused by multipath fading. Most carriers arestill windowed efficiently, albeit fluctuations occur around theexpected interference trend with outdated CIRs and PDPs, but theperformance recedes compared to current lengths due to the non-optimalwindowing as the CIRs of all users may have changed drastically.

As shown with reference to FIG. 5, the method of the present inventionmay be employed in system 200 comprising an OFDM transmitter 205 and/oran OFDM receiver 225. As shown with reference to FIG. 5, the OFDMtransmitter 205 includes a modulation module 210 configured to receiveincoming data and to generate an OFDM-based signal comprising aplurality of subcarriers. The OFDM transmitter 205 further includes anInverse Fast Fourier Transform (IFFT) module 215, operating as atransmitter filter to filter the subcarriers of the OFDM-based signalusing the proposed subcarrier specific based windowing scheme togenerate a filtered OFDM-based signal. The filtered OFDM-based signal isthen provided to a digital-to-analog module 220 of the transmitter priorto transmission of the filtered OFDM-based signal over the channel. Inaddition, the OFDM receiver 225 includes an analog-to-digital module 230configured to receive incoming OFDM-based signals comprising a pluralityof subcarriers that has been transmitted over the channel. Theanalog-to-digital module 230 provides the digital representation of theOFDM-based signals to a Fast Fourier Transform (FFT) module, operatingas a receiver filter 235 to filter the subcarriers of the OFDM-basedsignal using the proposed subcarrier specific windowing scheme of thepresent invention to generate a filtered OFDM-based signal. The filteredOFDM-based signal is then provided to a demodulation module 240 of thereceiver prior to transmission of the demodulated data over the channel.As such, the proposed windowing scheme utilizes the expected aggregateinterference power to determine subcarrier specific window lengths thatminimize the interference. Thus, maximum ACI and ISI suppression isachieved at the transmitter 205 and maximum ACI and ISI rejection isachieved at the receiver 225. Since transmit and receive windowing areindependent of each other, they can be used together or independently inthe transmitter 205 or the receiver 225.

With the present invention, expected and instantaneous interferencepowers have been determined. Interference power is used to determinesubcarrier specific window lengths (SSWs) that minimize theinterference. Numerous guidelines with various computationalcomplexities to determine optimal window lengths under insufficient CPhave been identified. The proposed subcarrier specific windowing schemeimproves SIR even when CP is insufficient. Average optimal windowlengths depend only on PDPs, and although instantaneous optimal windowlengths depend on users' CIRs, fluctuation is minimal. Therefore,subcarrier specific windowing outperforms fixed windowing, even withoutdated window lengths, such as in the case of powerful interferers.

Future wireless communication networks are planned to serviceasynchronous users in adjacent bands, utilizing reduced guard bands, inorder to be able to service as many users as possible and to reducelatencies. In various embodiments, the present invention enhancescommunication performance by adaptively mitigating the interference thatresults due to the reduction of both guard bands and guard times. Theembodiments of the invention help to enable high performancecommunication services while also increasing the number of served usersand reducing latencies and redundancies.

The various techniques described herein can be implemented in connectionwith hardware or software or, where appropriate, with a combination ofboth. Thus, the methods and system described herein, or certain aspectsor portions thereof, can take the form of program code (i.e.,instructions) embodied in tangible media, such as hard drives, solidstate drives, or any other machine-readable storage medium, wherein,when the program code is loaded into and executed by a machine, such asa computing device, the machine becomes an apparatus for practicing theinvention. In the case of program code execution on programmablecomputers, the computing device will generally include a processor, astorage medium readable by the processor (including volatile andnon-volatile memory and/or storage elements), at least one input device,and at least one output device. The program(s) can be implemented inassembly or machine language, if desired. In any case, the language canbe a compiled or interpreted language, and combined with hardwareimplementations.

The invention can also be practiced via communications embodied in theform of program code that is transmitted over some transmission medium,such as over electrical wiring or cabling, through fiber optics, or viaany other form of transmission, wherein, when the program code isreceived and loaded into and executed by a machine, such as an EPROM, agate array, a programmable logic device (PLD), a client computer, or thelike, the machine becomes an apparatus for practicing the invention.When implemented on a general-purpose processor, the program codecombines with the processor to provide a unique apparatus that operatesto invoke the functionality of the invention. Additionally, any storagetechniques used in connection with the invention can be a combination ofhardware and software.

It will be seen that the advantages set forth above, and those madeapparent from the foregoing description, are efficiently attained andsince certain changes may be made in the above construction withoutdeparting from the scope of the invention, it is intended that allmatters contained in the foregoing description or shown in theaccompanying drawings shall be interpreted as illustrative and not in alimiting sense.It will be seen that the advantages set forth above, andthose made apparent from the foregoing description, are efficientlyattained and since certain changes may be made in the above constructionwithout departing from the scope of the invention, it is intended thatall matters contained in the foregoing description or shown in theaccompanying drawings shall be interpreted as illustrative and not in alimiting sense.

It is also to be understood that the following claims are intended tocover all of the generic and specific features of the invention hereindescribed, and all statements of the scope of the invention which, as amatter of language, might be said to fall therebetween. Now that theinvention has been described,

What is claimed is:
 1. A method for windowing of an Orthogonal FrequencyDivision Multiplexing (OFDM)-based signal, the method comprising:receiving, at a receiver, an OFDM-based signal comprising a plurality ofsubcarriers; estimating an aggregate adjacent channel interference (ACI)and intersymbol interference (ISI) at each of the plurality ofsubcarriers; estimating an optimal window duration for each of theplurality of subcarriers, wherein the optimal window duration is theduration that minimizes the aggregate adjacent channel interference(ACI) and intersymbol interference (ISI) at each of the plurality ofsubcarriers; and performing, at the receiver, windowing of each of theplurality of subcarriers of the received OFDM-based signal bymultiplying each of the plurality of subcarriers by the optimal windowduration to generate a filtered OFDM-based signal.
 2. The method ofclaim 1, wherein the optimal window duration for each of the pluralityof subcarriers is an instantaneous optimal window duration and whereinestimating an optimal window duration for each of the plurality ofsubcarriers, wherein the optimal window duration is the duration thatminimizes the aggregate adjacent channel interference (ACI) andintersymbol interference (ISI) at each of the plurality of subcarriersusing power density profile (PDF) and channel impulse (CIR) for each ofthe plurality of subcarriers.
 3. The method of claim 1, wherein theoptimal window duration for each of the plurality of subcarriers is aninstantaneous average window duration and wherein estimating an optimalwindow duration for each of the plurality of subcarriers, wherein theoptimal window duration is the duration that minimizes the aggregateadjacent channel interference (ACT) and intersymbol interference (ISI)at each of the plurality of subcarriers using power density profile(PDF) for each of the plurality of subcarriers.
 4. The method of claim1, wherein estimating an optimal window duration for each of theplurality of subcarriers, wherein the optimal window duration is theduration that minimizes the aggregate adjacent channel interference(ACI) and intersymbol interference (ISI) at each of the plurality ofsubcarriers further comprises: estimating the aggregate ACI and ISI fora center subcarrier with no windowing; iteratively increasing a durationof the window of the center subcarrier and re-estimating the aggregateACI and ISI, until a longest duration window that does not increase theaggregate ACI and ISI is identified as the optimal window duration ofthe center subcarrier; setting durations of windows for subcarriersadjacent to the center subcarrier to be equal to the optimal windowduration of the center subcarrier; and iteratively increasing anddecreasing the duration of the window for the adjacent subcarriers untila longest duration window that does not increase the aggregate ACI andISI is identified as the optimal window duration of the adjacentsubcarriers.
 5. The method of claim 1, wherein the OFDM-based signal isequalized before estimating the aggregate ACI and ISI for each of theplurality of subcarriers.
 6. A method for windowing of an OrthogonalFrequency Division Multiplexing (OFDM)-based signal, the methodcomprising: receiving, at a transmitter, an OFDM-based signal comprisinga plurality of subcarriers; estimating an aggregate adjacent channelinterference (ACI) and intersymbol interference (ISI) at each of theplurality of subcarriers; estimating an optimal window duration for eachof the plurality of subcarriers, wherein the optimal window duration isthe duration that minimizes the aggregate adjacent channel interference(ACI) and intersymbol interference (ISI) at each of the plurality ofsubcarriers; performing, at the transmitter, windowing of each of theplurality of subcarriers of the received OFDM-based signal bymultiplying each of the plurality of subcarriers by the optimal windowduration to generate a filtered OFDM-based signal; and transmitting,from the transmitter, the filtered OFDM-based signal.
 7. The method ofclaim 6, wherein the optimal window duration for each of the pluralityof subcarriers is an instantaneous optimal window duration and whereinestimating an optimal window duration for each of the plurality ofsubcarriers, wherein the optimal window duration is the duration thatminimizes the aggregate adjacent channel interference (ACI) andintersymbol interference (ISI) at each of the plurality of subcarriersusing power density profile (PDF) and channel impulse (CIR) for each ofthe plurality of subcarriers.
 8. The method of claim 6, wherein theoptimal window duration for each of the plurality of subcarriers is aninstantaneous average window duration and wherein estimating an optimalwindow duration for each of the plurality of subcarriers, wherein theoptimal window duration is the duration that minimizes the aggregateadjacent channel interference (ACI) and intersymbol interference (ISI)at each of the plurality of subcarriers using power density profile(PDF) for each of the plurality of subcarriers.
 9. The method of claim6, wherein estimating an optimal window duration for each of theplurality of subcarriers, wherein the optimal window duration is theduration that minimizes the aggregate adjacent channel interference(ACI) and intersymbol interference (ISI) at each of the plurality ofsubcarriers further comprises: estimating the aggregate ACI and ISI fora center subcarrier with no windowing iteratively increasing a durationof the window of the center subcarrier and re-estimating the aggregateACI and ISI, until a longest duration window that does not increase theaggregate ACI and ISI is identified as the optimal window duration ofthe center subcarrier; setting durations of windows for subcarriersadjacent to the center subcarrier to be equal to the optimal windowduration of the center subcarrier; and iteratively increasing anddecreasing the duration of the window for the adjacent subcarriers untila longest duration window that does not increase the aggregate ACI andISI is identified as the optimal window duration of the adjacentsubcarriers.
 10. The method of claim 6, wherein the OFDM-based signal isequalized before estimating the aggregate ACI and ISI for each of theplurality of subcarriers.
 11. A receiver for windowing of an OrthogonalFrequency Division Multiplexing (OFDM)-based signal, the receivercomprising: an analog to digital module configured for receiving anOFDM-based signal comprising a plurality of subcarriers; a receiverfilter coupled to the analog to digital module, the receiver filterconfigured for estimating an aggregate adjacent channel interference(ACI) and intersymbol interference (ISI) at each of the plurality ofsubcarriers, for estimating an optimal window duration for each of theplurality of subcarriers, wherein the optimal window duration is theduration that minimizes the aggregate adjacent channel interference(ACI) and intersymbol interference (ISI) at each of the plurality ofsubcarriers and for performing windowing of each of the plurality ofsubcarriers of the received OFDM-based signal by multiplying each of theplurality of subcarriers by the optimal window duration to generate afiltered OFDM-based signal; and a demodulation module coupled to thereceiver filter, the demodulation module configured for receiving thefiltered OFDM-based signal and for demodulating each of the plurality ofsubcarriers of the OFDM-based signal.
 12. The receiver of claim 1,wherein the optimal window duration for each of the plurality ofsubcarriers is an instantaneous optimal window duration and whereinestimating an optimal window duration for each of the plurality ofsubcarriers, wherein the optimal window duration is the duration thatminimizes the aggregate adjacent channel interference (ACI) andintersymbol interference (ISI) at each of the plurality of subcarriersusing power density profile (PDF) and channel impulse (CIR) for each ofthe plurality of subcarriers.
 13. The receiver of claim 11, wherein theoptimal window duration for each of the plurality of subcarriers is aninstantaneous average window duration and wherein estimating an optimalwindow duration for each of the plurality of subcarriers, wherein theoptimal window duration is the duration that minimizes the aggregateadjacent channel interference (ACI) and intersymbol interference (ISI)at each of the plurality of subcarriers using power density profile(PDF) for each of the plurality of subcarriers.
 14. The receiver ofclaim 11, wherein estimating an optimal window duration for each of theplurality of subcarriers, wherein the optimal window duration is theduration that minimizes the aggregate adjacent channel interference(ACI) and intersymbol interference (ISI) at each of the plurality ofsubcarriers further comprises: estimating the aggregate ACI and ISI fora center subcarrier with no windowing; iteratively increasing a durationof the window of the center subcarrier and re-estimating the aggregateACI and ISI, until a longest duration window that does not increase theaggregate ACI and ISI is identified as the optimal window duration ofthe center subcarrier; setting durations of windows for subcarriersadjacent to the center subcarrier to be equal to the optimal windowduration of the center subcarrier; and iteratively increasing anddecreasing the duration of the window for the adjacent subcarriers untila longest duration window that does not increase the aggregate ACI andISI is identified as the optimal window duration of the adjacentsubcarriers.
 15. The receiver of claim 11, wherein the OFDM-based signalis equalized before estimating the aggregate ACI and ISI for each of theplurality of subcarriers.
 16. A transmitter for windowing of anOrthogonal Frequency Division Multiplexing (OFDM)-based signal, thetransmitter comprising: a modulation module configured to receive adigital signal to be transmitted, the modulation module configured tomodulate the digital signal to generate an OFDM-based signal comprisinga plurality of subcarriers; a transmitter filter coupled to themodulation module, the transmitter filter configured for estimating anaggregate adjacent channel interference (ACI) and intersymbolinterference (ISI) at each of the plurality of subcarriers, forestimating an optimal window duration for each of the plurality ofsubcarriers, wherein the optimal window duration is the duration thatminimizes the aggregate adjacent channel interference (ACI) andintersymbol interference (ISI) at each of the plurality of subcarriersand for performing windowing of each of the plurality of subcarriers ofthe received OFDM-based signal by multiplying each of the plurality ofsubcarriers by the optimal window duration to generate a filteredOFDM-based signal; and a digital to analog module coupled to thetransmitter filter, the digital to analog module configured fortransmitting the filtered OFDM-based signal.
 17. The transmitter ofclaim 16, wherein the optimal window duration for each of the pluralityof subcarriers is an instantaneous optimal window duration and whereinestimating an optimal window duration for each of the plurality ofsubcarriers, wherein the optimal window duration is the duration thatminimizes the aggregate adjacent channel interference (ACI) andintersymbol interference (ISI) at each of the plurality of subcarriersusing power density profile (PDF) and channel impulse (CIR) for each ofthe plurality of subcarriers.
 18. The transmitter of claim 16, whereinthe optimal window duration for each of the plurality of subcarriers isan instantaneous average window duration and wherein estimating anoptimal window duration for each of the plurality of subcarriers,wherein the optimal window duration is the duration that minimizes theaggregate adjacent channel interference (ACI) and intersymbolinterference (ISI) at each of the plurality of subcarriers using powerdensity profile (PDF) for each of the plurality of subcarriers.
 19. Thetransmitter of claim 16, wherein estimating an optimal window durationfor each of the plurality of subcarriers, wherein the optimal windowduration is the duration that minimizes the aggregate adjacent channelinterference (ACI) and intersymbol interference (ISI) at each of theplurality of subcarriers further comprises: estimating the aggregate ACIand ISI for a center subcarrier with no windowing; iterativelyincreasing a duration of the window of the center subcarrier andre-estimating the aggregate ACI and ISI, until a longest duration windowthat does not increase the aggregate ACI and ISI is identified as theoptimal window duration of the center subcarrier; setting durations ofwindows for subcarriers adjacent to the center subcarrier to be equal tothe optimal window duration of the center subcarrier; and iterativelyincreasing and decreasing the duration of the window for the adjacentsubcarriers until a longest duration window that does not increase theaggregate ACI and ISI is identified as the optimal window duration ofthe adjacent subcarriers.
 20. The transmitter of claim 16, wherein theOFDM-based signal is equalized before estimating the aggregate ACI andISI for each of the plurality of subcarriers.